Find the value after five years of a $3,000 savings account that pays 3% interest compounded yearly. Round the answer to two decimal places.
To find the value of the savings account after five years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
Given:
P = $3,000
r = 3% = 0.03
n = 1 (compounded yearly)
t = 5 years
Plugging these values into the formula, we get:
A = 3000(1 + 0.03/1)^(1*5)
A = 3000(1 + 0.03)^5
A = 3000(1.03)^5
A ≈ $3,462.94
Rounding the answer to two decimal places, the value of the savings account after five years is approximately $3,462.94.